Abstract: The purpose of this paper is to study the effect of the changes in the weights (w+ik, w-ik) of the deviational variables (ni, pi, ni+pi) in the achievement function of the Weighted Linear Goal Programming Problem (GPP). If the weights of the deviational variables associated with priority levels are increased/decreased Lee’s Modified Simplex method showed that an achievement level of unachieved priorities are decreased/increased respectively and the values of decision variables remain unchanged. While the standard simplex method showed that if the weights of the deviational variables are increased/decreased, an achievement level of the priorities are decreased/increased respectively, the values of decision variables remain unchanged for some weighting structures and there exist some other weighting structures for which the solution of GPP is changed. Thus Standard simplex method can be used for solution and sensitivity analysis of a particular class of WGPP.